RU2671620C1 - High-speed autocompensation scheme of quantum key distribution - Google Patents

Abstract

FIELD: cryptography.SUBSTANCE: invention relates to quantum cryptography, which lies in the field of information protection. Communication system for transmitting a cryptographic key between the ends of a channel includes a transmitting node comprising a beam splitter, an electro-optical attenuator, an amplitude modulator, a phase modulator, a storage line, a Faraday mirror, a synchronization detector; receiving unit containing laser, avalanche photodiodes, beam splitter, circulator, delay line, phase modulator, polarizing beam splitter, Mach-Zehnder interferometer; and a quantum channel for connecting the specified nodes. In this case, the storage line is placed between the electro-optical phase modulator of the sender and the Faraday mirror.EFFECT: technical result is an increase in the limiting frequency of the repetition of laser pulses at a fixed value of their width, which makes it possible to use an auto-compensating circuit at a frequency, the period of which is equal to the width of the laser pulse, which is the maximum possible result.3 cl, 3 dwg

Description

The invention relates to quantum cryptography in the field of information security.

State of the art

The prior art is known to US patent No. 6188768 "Self-compensation scheme of the quantum distribution of a cryptographic key based on polarized light separation", published February 13, 2001. This patent contains the basic information and technical solutions used for the auto-compensation optical scheme of quantum key distribution. In such an optical scheme, when pulses propagate back and forth, Rayleigh backscattering can significantly increase the noise recorded by detectors operating in the detection mode of single photons in the process of generating a quantum key. As a result, the pulses are sent in small packets, between which there are significant time pauses necessary for the passage of light through the circuit.

Also known is Automated 'plug and play' quantum key distribution, published in Electronics Letters (Volume: 34, Issue: 22, 29 Oct 1998). This article partially solved the above problem by adding a storage line on the sender side. However, it is necessary to modulate the pulses when moving in both directions due to the polarization sensitivity of the phase modulator. The relative position of the phase modulator and the Faraday mirror on the sender side in the above scheme imposes significant restrictions on the maximum pulse repetition rate

Technical challenge

The technical task is to modernize the self-compensation scheme of the quantum distribution of the key, in order to increase the maximum repetition rate of laser pulses at a fixed value of their width.

The technical result coincides with the task and allows the use of a self-compensation scheme at a frequency corresponding to a period equal to the width of the laser pulse, which is a fundamentally possible result.

Decision

The technical result is achieved through the use of a communication system for transmitting a cryptographic key between the ends of the channel, including

a) a transmitting node (Alice) containing a beam splitter, an electro-optical attenuator, an amplitude modulator, a phase modulator, a storage line, a Faraday mirror, a synchronization detector,

b) a receiving unit (Bob) containing a laser, avalanche photodiodes, a beam splitter, a circulator, a delay line, a phase modulator, a polarizing beam splitter, a Mach-Zendner interferometer,

c) as well as a quantum channel for connecting these nodes,

wherein the storage line is placed between the sender's electro-optical phase modulator and the Faraday mirror. Changing the position of the storage line eliminates the intersection on the phase modulator of the sender of pulses traveling in different directions. As a result, it becomes possible to increase the pulse repetition rate to the maximum permissible value. The maximum permissible frequency value corresponds to a period equal in duration to the pulse width at the base. A further increase in the frequency will entail the mutual overlapping of adjacent pulses, which will lead to an increase in the level of errors in the final key.

In the given analogs, the time of movement of pulses from the phase modulator to the Faraday mirror and vice versa is significantly shorter than the time of the train of pulses, which leads to the superposition of signals going in different directions on the phase modulator. Thus, for the correct modulation of the states transmitted by the sender, it is necessary to make time intervals between the pulses in the train, so as to exclude the overlapping of incoming and reflected pulses. This leads to a decrease in the key sending speed.

Description of drawings

In FIG. 1 shows a self-compensation scheme of a quantum key distribution in the proposed modification. The following notation is introduced.

Transmitting Node (Alice). Beam splitter 11; electro-optical attenuator 12; amplitude modulator 13; phase modulator 14; storage line 15; Faraday mirror 16; sync detector 17.

Receiving Node (Bob). Laser 1; circulator 2; avalanche photodiodes 3, 4; a beam splitter 5; phase modulator 6; delay line 7; Mach-Zendner interferometer 8; polarizing beam splitter 9.

Quantum Channel 10.

In FIG. Figure 2 shows the model of pulse repetition before and after reflection from the Faraday mirror in the self-compensation scheme in the initial configuration. Solid lines indicate incoming pulses, and dashed - reflected.

In FIG. Figure 3 shows a model of the pulse sequence before and after reflection from a Faraday mirror in the presented modification of the self-compensation scheme. Solid lines indicate incoming pulses, and dashed - reflected.

Detailed description

The self-compensation scheme consists of a transmitter and a receiver (in cryptography traditionally called Alice and Bob, respectively), which are interconnected by a single-mode optical fiber. The transmission of optical signals is organized as follows.

The laser on the Bob side emits a multi-photon optical pulse with linear polarization in the spectral range in the region of 1550 nm, which passes through the circulator 2 (Fig. 1) and is sent to the beam splitter 5. The function of the circulator is to direct the light to the necessary outputs. From the laser, he transfers it to the beam splitter 5, and when the light comes back from the beam splitter 5, it directs it to the detector 3. The circulator can be made in the form of a fiber-optic element on a crystal.

Next, one part of the pulse is fed to the input of the polarizing beam splitter 9 along the short arm of the Mach-Zehnder fiber optic interferometer (8). The second part of the pulse arrives at the polarization beam splitter 9, having passed the long arm formed by the delay line and the fiber optic phase modulator 6. The optical elements in the long arm are made of polarization-supporting fiber. This makes it possible to orient the radiation polarization so that both parts of the pulse exit through the output of the polarizing beam splitter 9 and go from Bob to Alice along an extended single-mode optical fiber (traditionally called a quantum communication channel (10)).

After passing through the quantum channel, the laser pulse enters Alice’s input, passes the phase modulator 14, the storage line 15, and is reflected from the Faraday mirror 16, which rotates the radiation polarization by 90 ° to automatically compensate for the polarization distortions of the optical fiber. On the way back, at the exit from Alice, the laser pulse is attenuated by the tunable attenuator 12 to a single-photon state (the average number of photons per pulse is 0.1-0.3). The photons returning from Alice to Bob have linear polarization rotated 90 °, so they are sent to the other arm of the interferometer by the input polarizing beam splitter 9, after which they are connected at the output where they interfere. The result of interference is recorded by an avalanche photodiode 4 in one shoulder or, after passing through a circulator 2, on an avalanche photodiode 3 in another shoulder. Since these two parts of the pulse travel the same path, and in reverse order inside Bob, this interferometer is automatically compensated.

To implement the BB84 protocol, Alice, using a phase modulator 14, applies a phase shift of 0 or π (first basis), and π / 2 or 3π / 2 (second basis) to the light pulse received from Bob at the right time. Since after passing through the quantum channel, the pulse has a random polarization, and the phase modulator works only along the selected direction, Alice performs modulation twice for each pulse - first, on the way to the Faraday 16 mirror, and then when moving in the opposite direction, with the polarization turned. Bob, having received single photons reflected from Alice, randomly selects a basis for measurement by applying a shift of 0 (first basis) or π / 2 (second basis) to his phase modulator 6 at the corresponding moment in time.

In such an optical scheme, when pulses propagate back and forth, Rayleigh backscattering can significantly increase the noise detected by detectors 3 and 4 operating in the mode of recording single photons in the process of generating a quantum key. Therefore, the laser does not emit pulses continuously, but sends trains of pulses in each transmission cycle, and the length of these trains corresponds to the length of the storage line 15 installed for this purpose in Alice’s optical circuit. Due to this, single-photon pulses propagating back no longer intersect in the quantum channel with multiphoton pulses traveling from Bob to Alice. So, for a storage line 25 km long, the train of pulses contains 120,000 pulses at a clock frequency of sending laser pulses of 500 MHz.

The process of generating a quantum key is as follows. At the first stage, calibration and tuning of the fiber optic communication channel is performed. To do this, the optical channel length is accurately measured using multiphoton pulses from Bob, while Alice’s adjustable attenuator 12 is set to full transmission. Bob receives the reflected signal and based on these measurements sets the position in time of the strobe for detectors 3 and 4, when they should register the signal. In this case, the detectors operate in the linear mode of registration of multiphoton light pulses.

After that, the quantum key generation mode is set. The reverse voltage on the avalanche photodiodes rises above the threshold breakdown voltage, and they switch to the registration mode for single photons (Geiger pulse counting mode). Bob emits a train of laser pulses. Next, Alice’s beam splitter 11 sends part of the radiation power of the incoming light pulses to the synchronization detector 17. It generates a trigger signal, which is used to synchronize Alice with Bob. Synchronization allows Alice to apply an electrical pulse to the phase modulator at the right time to modulate the phase of the optical pulse, in accordance with the BB84 protocol. Alice's attenuator 12 is open for transmission. When the train of pulses fills the storage line 15, this fast, electrically controlled, attenuator reduces its transmission to such a level that light pulses with a photon content of 0.1-0.3 photons per pulse go from Alice to Bob. Under such conditions, the probability P _{n of} finding n photons in a laser pulse obeys Poisson statistics:

- среднее число фотонов в импульсе. В квантовой криптографии импульс считается однофотонным, если

находится в пределах 0,1-0,2. Так, для

, доля импульсов с двумя фотонами составляет 5% от однофотонных, а с тремя фотонами - 0.16%. Практически, в этом случае из каждых 10 импульсов в 9 нет ни одного фотона.Where

is the average number of photons per pulse. In quantum cryptography, a pulse is considered to be single-photon if

is in the range of 0.1-0.2. So, for

, the fraction of pulses with two photons is 5% of single-photon, and with three photons - 0.16%. Practically, in this case, out of every 10 pulses in 9, there is not a single photon.

Alice remembers the serial number of each pulse and the value applied by means of a phase modulator. Bob writes to the buffer and sends to the computer both the pulse serial number and the basis for measuring single photons detected by detectors 3 and 4. Based on these data, using the open channel between their computers, Alice and Bob form the same quantum key.

Electro-optical phase modulators add a phase shift along the selected polarization direction of the transmitted radiation. Since after passing the quantum channel, the polarization will randomly change due to external influences, the pulse arriving at the Alice phase modulator will have a random polarization state. Thus, its phase will be modulated only partially - along one of the components. However, the rotation of the radiation polarization by 90 ° with the Faraday mirror allows you to apply the necessary phase shift to the orthogonal component, at the time of the pulse in the opposite direction. As a result, the correct modulation can be carried out if the same phase shift on the modulator is applied when the pulse moves in both directions.

The difference between the above scheme and prototype 2 is to change the location of the storage line on the side of Alice. In the prototype configuration, it is necessary that the time between adjacent pulses in the train be longer than the pulse propagation time through the crystal, it is also necessary to precisely select the distance between the modulator and the Faraday mirror so that incoming and reflected pulses do not pass through the modulator at the same time, otherwise it becomes it’s impossible to assign them different, randomly selected phases. The time interval between pulses in the train increases the period of their repetition, thereby reducing the frequency and the final rate of key generation.

The key sending speed is expressed as:

Where s is the duty cycle of the trains, equal to the ratio of the train time to the period of their movement, T is the duration of one train of pulses, v is the pulse repetition rate within one train. The duration of the train is determined by the length of the storage line used on the receiver side:

Where l is the length of the storage line, n is the refractive index of the optical fiber, and c is the speed of light in vacuum.

The maximum pulse repetition rate in the given configuration as seen in FIG. 2 is determined by the doubled length of the crystal in the modulator, since it is necessary to spatially separate the pulses traveling in different directions. In this way:

Where t _m is the time of the pulse through the crystal of the phase modulator.

Thus, the final formula for the key sending speed is:

In the proposed solution, the storage line 15 is located between the phase modulator of Alice and the Faraday mirror. Thus, the entire train of pulses first passes through the phase modulator in one direction, falling into the storage line, and then, reflected, in the same order passes in the opposite direction. In this configuration, pulses moving in the forward and reverse directions never intersect on the modulator, which allows them to be located as close to each other as possible, increasing the repetition rate to the maximum possible for a given pulse width, as shown in FIG. 3. Thus, the pulse repetition rate in the proposed configuration is equal to:

where t _p is the pulse repetition period.

Since the modification does not affect other parameters of the scheme, the final key sending speed:

A typical crystal length, such as lithium niobate (LiNbO ₃ ), in electro-optical modulators is about 7 cm. Thus, the time of light movement in the crystal is about 500 ps. With the help of modern electronics (programmable logic integrated circuits), it is possible to generate substantially shorter (100 ps or less) laser pulses. With the above parameters, the key sending speed in the auto-compensation scheme increases by more than 10 times.

The proposed modification can significantly increase the maximum repetition rate of laser pulses, without affecting the other parameters of the circuit. This significantly increases the maximum key sending speed.

Claims (7)

1. A communication system for transmitting a cryptographic key between the ends of the channel, including: - a receiving unit containing a laser, at least two avalanche photodiodes, a beam splitter, a circulator, a delay line, a phase modulator, a polarizing beam splitter, a Mach-Zendner interferometer, while these elements are optically connected to each other so that the optical pulse from the laser passes through a circulator optically connected to the second avalanche photodiode and a polarizing beam splitter, on the short arm of the Mach-Zehnder interferometer and on the long arm formed by the delay line, a phase modulator, - a transmitting node containing a beam splitter optically interconnected, an electro-optical attenuator, an amplitude modulator, a phase modulator, a storage line, a Faraday mirror, the beam splitter output being optically connected to a synchronization detector, - as well as a quantum channel that connects the polarizing beam splitter of the receiving node with the beam splitter of the transmitting node, characterized in that the storage line is placed between the electro-optical phase modulator of the sender and the Faraday mirror. 2. The system according to claim 1, characterized in that the laser emits light at a telecommunication wavelength of 1555 nm. 3. The system according to claim 1, characterized in that electro-optical modulators based on a lithium niobate crystal (LiNbO ₃ ) are used to change the phase.

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